Question

A researcher believes that 12% of a simple random sample of adults will be able to identify a Toyota Scion by brand and model name. The researcher wishes to estimate with 95% confidence and an allowance for error no greater than 2.5%. How large should the sample be?

Answer 1

Answer: 650

Step-by-step explanation:

When prior estimate of population proportion is known , then the formula to find the required sample size is given by :-

$n=p(1-p)(\dfrac{z^*}{E})^2$

, where p= population proportion

E= margin of error

z* = Critical value.

Let p be the proportion of adults able to identify a Toyota Scion by brand and model name.

As per given , we have

p = 12%= 0.12

E= 2.5%=0.025

Critical value for 95% confidence interval : z* = 1.960  [By z-table ]

Then, the required sample size = $n=(0.12)(1-(0.12))(\dfrac{1.96}{0.025})^2$

$n=(0.1056)(78.4)^2$

$n=(0.1056)(6146.56)$

$n=649.076736\approx650$

Thus , the required sample size = 650